Expression of type Lambda

from the theory of proveit.numbers.divisibility

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, x, y, z
from proveit.logic import And, Equals, InSet
from proveit.numbers import Divides, GCD, Integer, Mult, one

# build up the expression from sub-expressions
expr = Lambda([x, y, z], Conditional(Divides(x, z), And(InSet(x, Integer), InSet(y, Integer), InSet(z, Integer), Divides(x, Mult(y, z)), Equals(GCD(x, y), one))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x, y, z\right) \mapsto \left\{x \rvert z \textrm{ if } x \in \mathbb{Z} ,  y \in \mathbb{Z} ,  z \in \mathbb{Z} ,  x \rvert \left(y \cdot z\right) ,  gcd\left(x, y\right) = 1\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	30, 31, 29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	30, 29
6	Literal
7	ExprTuple	8, 9, 10, 11, 12
8	Operation	operator: 15 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 19 operands: 20
13	ExprTuple	30, 21
14	ExprTuple	31, 21
15	Literal
16	ExprTuple	29, 21
17	Literal
18	ExprTuple	30, 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	31, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable